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-Nonlinear Stability of Nonlocalized Modulated Periodic Reaction-Diffusion Waves

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  • Soyeun Jung

Abstract

Assuming spectral stability conditions of periodic reaction-diffusion waves , we consider -nonlinear stability of modulated periodic reaction-diffusion waves, that is, modulational stability, under localized small initial perturbations with nonlocalized initial modulations. -nonlinear stability of such waves has been studied in Johnson et al. (2013) for by using Hausdorff-Young inequality. In this note, by using the pointwise estimates obtained in Jung, (2012) and Jung and Zumbrun (2016), we extend -nonlinear stability ( ) in Johnson et al. (2013) to -nonlinear stability. More precisely, we obtain -estimates of modulated perturbations of with a phase function under small initial perturbations consisting of localized initial perturbations and nonlocalized initial modulations .

Suggested Citation

  • Soyeun Jung, 2017. "-Nonlinear Stability of Nonlocalized Modulated Periodic Reaction-Diffusion Waves," Advances in Mathematical Physics, Hindawi, vol. 2017, pages 1-7, November.
    • Handle: RePEc:hin:jnlamp:3824501
    DOI: 10.1155/2017/3824501
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